= Solution
{c}
Buy $1/F_0^T$ shares and take a short <forward contract> for $1/F_0^T$ shares at delivery price $F_0^T$. The forward has zero initial value, and the combined terminal payoff is
$$
\frac{S_T}{F_0^T}+\frac{F_0^T-S_T}{F_0^T}=1.
$$
Therefore the <synthetic zero-coupon bond> has initial price
$$
\boxed{P(0,T)=\frac{S_0}{F_0^T}.}
$$
Its implied continuously compounded maturity yield is $r_T=T^{-1}\log(F_0^T/S_0)>0$.
To replicate a constant-rate <risk-free asset> throughout the interval, the market must support dynamically coherent discounting, not just this one terminal payment. A sufficient condition is that for all $0\leq t\leq u\leq T$ the fair forward prices satisfy $F_t^u=S_te^{r(u-t)}$ for the same deterministic $r>0$, with the required stock/forward positions tradable and no intervening payments. Then $P(t,u)=S_t/F_t^u=e^{-r(u-t)}$, and a suitably scaled fixed-maturity <zero-coupon bond> grows deterministically as $e^{rt}$. A single initial forward quote does not establish these intermediate-time conditions; even a flat initial yield curve need not imply deterministic future rates.
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